r^2-4r=3r+30

Solution for r^2-4r=3r+30 equation:

Simplifying
r2 + -4r = 3r + 30

Reorder the terms:
-4r + r2 = 3r + 30

Reorder the terms:
-4r + r2 = 30 + 3r

Solving
-4r + r2 = 30 + 3r

Solving for variable 'r'.

Reorder the terms:
-30 + -4r + -3r + r2 = 30 + 3r + -30 + -3r

Combine like terms: -4r + -3r = -7r
-30 + -7r + r2 = 30 + 3r + -30 + -3r

Reorder the terms:
-30 + -7r + r2 = 30 + -30 + 3r + -3r

Combine like terms: 30 + -30 = 0
-30 + -7r + r2 = 0 + 3r + -3r
-30 + -7r + r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
-30 + -7r + r2 = 0

Factor a trinomial.
(-3 + -1r)(10 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-3, 10}